Parameter Reconstruction for Biochemical Networks Using Interval Analysis

Abstract

In recent years, the modeling and simulation of biochemical networks has attracted increasing attention. Such networks are commonly modeled by systems of ordinary differential equations, a special class of which are known as S-systems. These systems are specifically designed to mimic kinetic reactions, and are sufficiently general to model genetic networks, metabolic networks, and signal transduction cascades. The parameters of an S-system correspond to various kinetic rates of the underlying reactions, and one of the main challenges is to determine approximate values of these parameters, given measured (or simulated) time traces of the involved reactants. Due to the high dimensionality of the problem, a straight-forward optimization strategy will rarely produce correct parameter values. Instead, almost all methods available utilize genetic/evolutionary algorithms to perform the non-linear parameter fitting. We propose a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. The proposed method can in principle be applied to any system of finitely parameterized differential equations, and, as we demonstrate, yields encouraging results for low dimensional S-systems.